Research context
GTFS
The introduction of the General Transit Feed Specification (GTFS) and widespread release of schedule data in this format has helped towards making transit metrics more broadly available and useable. GTFS is an open, text-based format that was developed originally to allow transit information to be included in the Google Maps navigation platform (MobilityData undatedMobilityData. undated. General Transit Feed Specification (GTFS). {https://gtfs.org/}.). The data structure is shown in the below figure.
GTFS entity relationship diagram. Source: adapted by author from Alamri et al (2023) and the GTFS Schedule Reference (16/11/2023 revision).
In the Entity Relationship Diargram (ERD) shown above, each box represents a database table in the GTFS, with table rows indicating the variables (columns) included in each1 For example, each record in the ‘stops’ table includes a value for stop_id, stop_name, stop_lat and stop_lon.. Relationships between the tables are indicated by the connecting lines, and Primary Key (PK) and Foreign Key (FK) designations2 For example, stop_id also appears in the ‘stop_times’ table as a Primary Key and Foreign Key.. “Crow’s feet” indicate the relationships between each table3 See https://i.stack.imgur.com/fxaAq.png for guide to the symbols. But, for example, the stops table is required, with the stop_id field providing a unique (primary) key for every stop. Within the stop_times table (which is also required) the stop_id field is a foreign key. Each unique stop_id can appear many times in the stop_times table, but must appear only once in the stops table. In the stop_times table each combination of trip_id, stop_id and arrival time must be unique (But, see note 2!) meaning that these fields represent a composite key..
The Transit Suppy Index
\[\begin{equation} SI_{area, time} = \sum{\frac{Area_{Bn}}{Area_{area}}*SL_{n, time}} \end{equation}\]
The Transit Supply Index (SI) was developed by Currie and Senbergs (2007Currie, Graham, and Zed Senbergs. 2007. “Identifying spatial gaps in public transport provision for socially disadvantaged Australians: the Melbourne needs-gap study.” Australasian Transport Research Forum.). Its equation is shown in the margin4 (1) \(SI_{area, time}\) is the Supply Index for the area of interest and a given period of time; (2) \(Area_{Bn}\) is the buffer area for each stop (n) within the area of interest. In Currie and Senbergs (2007) this was based on a radius of 400 metres for bus and tram stops, and 800 metres for railway stations; (3) \(Area_{area}\) is the area of the area of interest; and (4) \(SL_{n,time}\) is the number of transit arrivals for each stop for a given time period. Minor adjustments have been made to generalise the equation, as Currie and Senbergs (2007) focus was the context of Melbourne’s Census Collection Districts (CCD) and calculations based on a week of transit service. CCDs predate the introduction of Statistical Areas 1, 2, 3, and 4 (SA1, SA2, SA3, SA4), and other geographical divisions currently used by the Australian Bureau of Statistics (ABS), which may be more familiar to readers.
An advantage of the SI is that it is a relatively simple number to calculate, understand and explain. It describes the number of transit arrivals at stops within an area of interest and time frame, multiplied by a factor accounting for the proportion of the area of interest that is within typical walking distance of each stop. Hence, more services, more stops and higher frequencies would all increase the SI score.
Simplicity is also helped by the way that the Index is additive. \(SI_{area, time}\) scores can be aggregated to calculate an overall score across multiple time periods or for a region encompassing multiple areas of interest.
gtfssupplyindex R package
R (R Core Team 2023R Core Team. 2023. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.) is a widely used and readily available statistical programming language. This was adopted for development of a package of functions and tools to calculate SI scores from a GTFS dataset. The package development setup and workflow described by Wickham and Bryan (2023Wickham, Hadley, and Jennifer Bryan. 2023. R Packages. " O’Reilly Media, Inc.". https://r-pkgs.org/.) was adopted. The package is available and documented on github (Reynolds 2024Reynolds, James. 2024. “Gtfssupplyindex.” https://github.com/James-Reynolds/gtfssupplyindex.).
The structure and functions used to generate each table are shown in the below Entity Relationship Diagram (ERD).
Entity Relationship Diagram (ERD) showing the data structure and functions of the gtfssupplyindex package
The package takes input from three files:
- a gtfs feed (gtfs.zip)
- a sf object describing the geometry of the areas for which the SI is to be calculated
- a csv file defining the buffer zone distances (in metres) for each route_type - a version of this file is included in the package.
The ultimate goal of the functions included in the gtfssupplyindex package is to output either a si_by_area table (bottom row, second from right) or the si_by_area_and_hour table (bottom right). which reports the SI score for each hour of the day across dates specified by the user.
Included in the package is an example GTFS dataset from the Mornington Penninsula Tourist Railway. The output (si_by_area_and_hour) table is shown as an example below.
Mornington Penninsula Tourist Railway hourly SI values for December 30, 2018, for SA1 zones, first six entries — THIS IS WHAT THE si_by_area_and_hour TABLE LOOKS LIKE
| area_id | SI | hour_starting |
|---|---|---|
| 214021381 | 0.0000672 | 10:00 |
| 214021385 | 0.0000000 | 10:00 |
| 214021591 | 0.2436873 | 10:00 |
| 214021592 | 0.0684965 | 10:00 |
| 214021381 | 0.0522962 | 11:00 |
| 214021385 | 0.0067970 | 11:00 |
Mornington Penninsula Tourist Railway hourly SI values for December 30, 2018, for SA1 zones, by hour — THIS IS A ‘WIDER’ VERSION OF THE si_by_area_and_hour TABLE
| area_id | 10:00 | 11:00 | 12:00 | 13:00 | 14:00 | 15:00 |
|---|---|---|---|---|---|---|
| 214021381 | 0.0000672 | 0.0522962 | 0.0523635 | 0.0000672 | 0.0522962 | 0.0523635 |
| 214021385 | 0.0000000 | 0.0067970 | 0.0067970 | 0.0000000 | 0.0067970 | 0.0067970 |
| 214021591 | 0.2436873 | 0.1366432 | 0.3803305 | 0.1366432 | 0.2436873 | 0.3803305 |
| 214021592 | 0.0684965 | 0.0000000 | 0.0684965 | 0.0000000 | 0.0684965 | 0.0684965 |
The upper table shows first six entries in the ‘longer’ version of the table. Each record shows the SI score for a unique combination of area_id5 Here the SA1 2021 zones and hour_starting6 The Mornington Penninsula Railway only runs between 10am and 4pm on the day in question.. The lower table shows the same data, but in a ‘wider’ format so that all hour_starting SI scores a visible7 As the Mornington Penninsula Railway has only 3 stops, only 5 SA1 2021 zones have SI scores.. Further details of the Mornington Penninsula Railway calculations8 Including hand verification. are available in the package documentation on github(Reynolds 2024Reynolds, James. 2024. “Gtfssupplyindex.” https://github.com/James-Reynolds/gtfssupplyindex.).
